Control Systems Theory

Broadly speaking, a fundamental problem in control theory is to automatically generate the control input that acts on the behaviour of such system in the best possible way. This is done by minimizing a cost criterion or performance index which penalises i) the deviations of key measurements from their desired values and ii) the control effort, because energy has its price: this is in particular the goal of optimal control. This very general setting has generated a large amount of literature connecting this problem with a broad circle of ideas encompassing Passivity, Spectral factorization, Riccati equations, and Stochastic realization. In recent years these ideas have been connected to Negative Imaginary Systems that models an important form o passivity in the case of systems where sensors and actuators a co-located. The study of these topics is a fundamental step for the design of control systems with high performances.

The research focuses on the analysis of the main theoretical properties of this class of systems, both in the continuous and in the discrete time cases, with possible applications in the context of drug treatment modeling, fluid systems and thermal models. Ongoing projects are the following:

Stability and stabilizability analysis

Stabilization by means of various classes of Lyapunov functions

Reachability analysis

Compartmental switched systems

Use of the stabilizability analyis in the context of viral mutation dynamics modeling under drug treatment